The Symmetric Regularized-Long-Wave equation: Well-posedness and nonlinear stability

The focus of the present work is the Symmetric Regularized-Long-Wave equation. We prove that the initial value problem for this equation is locally and globally well-posed in H per s × H per s − 1 and H s ( R ) × H s − 1 ( R ) , if s ≥ 0 . We also prove the existence and nonlinear stability of periodic travelling wave solutions, of cnoidal type, for the equation mentioned above.